Question

Find the given angle measure for regular hexagon ABCDEF.

I would like all 4 answers and how to get them (show work).

Thanks!

Answer 1

The measure of each angle in a regular hexagon is 120 degrees.

Step-by-step explanation:

A regular hexagon has six equal sides and six equal angles. To find the measure of each angle in a regular hexagon, we can use the formula:

Angle measure = 180 * (n-2) / n

where n is the number of sides of the polygon. Substituting n = 6, we get:

Angle measure = 180 * (6-2) / 6 = 180 * 4 / 6 = 120 degrees

So, each angle in a regular hexagon measures 120 degrees. Therefore, the given angle measure for hexagon ABCDEF is 120 degrees.

Answer 2

Question 12: 60°

Question 13: 30°

Question 14: 60°

Question 15: 120°

Step-by-step explanation:

Question 12: The measure of a circle is 360°, so ∠CGD which is
`(1)/(6)` of a full rotation is 60°.

Question 13: ∠CGH is
`(1)/(2)` of ∠CGD, so its angle measure is 30°.

Question 14: Since the interior sum of all angles in a triangle is 180° and two angles have measures of 90° and 30°, that means ∠HCG has a measure of 60°.

Question 15: Since ∠EGC is
`(1)/(3)` of a full rotation, and is twice as great as ∠CGD, that means it has an angle measure of 120°.